| # Licensed to the Apache Software Foundation (ASF) under one or more |
| # contributor license agreements. See the NOTICE file distributed with |
| # this work for additional information regarding copyright ownership. |
| # The ASF licenses this file to You under the Apache License, Version 2.0 |
| # (the "License"); you may not use this file except in compliance with |
| # the License. You may obtain a copy of the License at |
| # |
| # http://www.apache.org/licenses/LICENSE-2.0 |
| # |
| # Unless required by applicable law or agreed to in writing, software |
| # distributed under the License is distributed on an "AS IS" BASIS |
| # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| # See the License for the specific language governing permissions and |
| # limitations under the License. |
| |
| # P-values for the two-sample Kolmogorov-Smirnov distribution: |
| # D = sup_x |F_m(x) - G_n(x)| |
| # D+ = sup_x F_m(x) - G_n(x) |
| # Computed using scipy.stats.kstest using arrays with configured overlap: |
| |
| # from scipy.stats import kstest |
| # import random |
| # |
| # def ksp(x, size=0): |
| # """ |
| # Given x representing steps on a 2D path taking the n-th step on x, |
| # generate y taking the other steps. |
| # The arrays are used for the KS test: |
| # x = [2, 3, 6] |
| # y = [0, 1, 4, 5] |
| # |
| # x = [0, 2, 3, 6] |
| # y = [1, 4, 5] |
| # |
| # The optional combined size of x and y can be used to fill y beyond |
| # the max value in x: |
| # x = [0, 2, 3, 6], size = 9 |
| # y = [1, 4, 5, 7, 8] |
| # """ |
| # assert min(x) >= 0 |
| # a = set(x) |
| # y = [v for v in range(max(size, max(x))) if v not in a] |
| # x = sorted(list(a)) |
| # (d, p2) = kstest(x, y, method='exact', alternative='two-sided') |
| # (dp, p1p) = kstest(x, y, method='exact', alternative='greater') |
| # (dm, p1m) = kstest(x, y, method='exact', alternative='less') |
| # m, n = len(x), len(y) |
| # if m > n: |
| # m, n = n, m |
| # print(n, m, round(d*n*m), p2, p1p if dp > dm else p1m) |
| # |
| # def kspr(n, m, k): |
| # """ |
| # Output k random samples for the KS statistic for size m+n |
| # """ |
| # assert m <= n |
| # x = list(range(m+n)) |
| # while k: |
| # k = k - 1 |
| # random.shuffle(x) |
| # ksp(x[0:n], size=m+n) |
| # |
| # def kspr2(n, m, k, steps=1): |
| # """ |
| # Output k random sample for the KS statistic for size m+n |
| # where steps is the number of random steps away from the most |
| # extreme d value. With a small k there is not much random |
| # selection among possible values. |
| # """ |
| # assert m <= n |
| # x = list(range(n+steps)) |
| # while k: |
| # k = k - 1 |
| # random.shuffle(x) |
| # ksp(x[0:n], size=m+n) |
| # |
| # m, n, D*m*n, p(D >= d), p(D+ >= d) |
| # kspr(100, 40, 20) |
| 40 100 340 0.9773418270040279 0.6329024797499111 |
| 40 100 860 0.12677239988246672 0.06339825886035746 |
| 40 100 580 0.5473896135904249 0.2794401566979873 |
| 40 100 880 0.11154244485514381 0.055778250027573084 |
| 40 100 480 0.770492146516542 0.41338818994955673 |
| 40 100 460 0.8119415167694873 0.44305520608128046 |
| 40 100 700 0.3164264340698098 0.1587740147927427 |
| 40 100 900 0.09783730779454616 0.04892267422427221 |
| 40 100 640 0.42307844481855844 0.21344392995383454 |
| 40 100 680 0.349817735774034 0.17576427607315334 |
| 40 100 480 0.770492146516542 0.41338818994955673 |
| 40 100 1240 0.006616625176172374 0.0033083126170043243 |
| 40 100 500 0.7267073322941818 0.3843233816008394 |
| 40 100 780 0.2052795987967731 0.10273149023483952 |
| 40 100 420 0.8856659279989376 0.5048023299540044 |
| 40 100 480 0.770492146516542 0.41338818994955673 |
| 40 100 620 0.46275830805993134 0.23416423523770283 |
| 40 100 760 0.22982383866844353 0.1150592615825157 |
| 40 100 820 0.16229871881876692 0.08118354558617719 |
| 40 100 420 0.8856659279989376 0.5048023299540044 |
| # kspr2(100, 40, 5, steps=30) |
| 100 40 1280 0.0045434627365337 0.00227173137342205 |
| 100 40 1380 0.0016788158396986734 0.000839407919897205 |
| 100 40 1120 0.018951512042934323 0.009475759289379455 |
| 100 40 1100 0.02233981664838027 0.011169915063692467 |
| 100 40 1080 0.02625373376387981 0.013126880631872185 |
| # kspr2(100, 40, 5, steps=25) |
| 100 40 1500 0.000456660920000192 0.0002283304600001775 |
| 100 40 1500 0.000456660920000192 0.0002283304600001775 |
| 100 40 1500 0.000456660920000192 0.0002283304600001775 |
| 100 40 1540 0.00028815415241434557 0.00014407707620718067 |
| 100 40 1640 8.590792015892992e-05 4.2953960079464965e-05 |
| # kspr2(100, 40, 5, steps=20) |
| 100 40 2020 3.855912283854308e-07 1.9279561419271548e-07 |
| 100 40 2000 5.299027236844599e-07 2.6495136184222997e-07 |
| 100 40 2080 1.451368666967504e-07 7.25684333483752e-08 |
| 100 40 2160 3.730939832822896e-08 1.8654699164114477e-08 |
| 100 40 2140 5.271510978784155e-08 2.6357554893920777e-08 |
| # kspr(100, 90, 20) |
| 100 90 660 0.9403465424443764 0.5673160110547633 |
| 100 90 1800 0.03830453866332627 0.019152364596527083 |
| 100 90 1000 0.5572530591243455 0.28499738340467284 |
| 100 90 1600 0.08683950302755603 0.04342261303057448 |
| 100 90 1280 0.2630149823414606 0.13178421976099924 |
| 100 90 890 0.6981836033061721 0.3666544765572714 |
| 100 90 750 0.8640266306725287 0.48568869295379447 |
| 100 90 920 0.6600778211517683 0.34362597484673946 |
| 100 90 1330 0.2248787518023298 0.11258453521977592 |
| 100 90 1120 0.41538876587262696 0.2095295198840798 |
| 100 90 970 0.595209186537845 0.3060980999853577 |
| 100 90 970 0.595209186537845 0.3060980999853577 |
| 100 90 830 0.7740517546485187 0.4162869563189197 |
| 100 90 950 0.6212031461485229 0.32090932344109196 |
| 100 90 900 0.6854565207494886 0.3588502088357719 |
| 100 90 1130 0.4045155234733332 0.20390002705223875 |
| 100 90 930 0.6472160884908673 0.336034954438692 |
| 100 90 1220 0.31466150497698403 0.15790996062322848 |
| 100 90 2170 0.006517639537689413 0.00325881982265406 |
| 100 90 1390 0.18483598432221077 0.09248275733380223 |
| # kspr2(100, 90, 5, steps=70) |
| 100 90 2000 0.015330694330104906 0.007665349189785158 |
| 100 90 2280 0.0036074485067851053 0.0018037242575994195 |
| 100 90 2000 0.015330694330104906 0.007665349189785158 |
| 100 90 2340 0.002579705416961608 0.0012898527094708143 |
| 100 90 2320 0.0028877356007539663 0.00144386780196359 |
| # kspr2(100, 90, 5, steps=65) |
| 100 90 2600 0.0005435137234678029 0.000271756861734953 |
| 100 90 2700 0.00028527869952446285 0.0001426393497622857 |
| 100 90 2610 0.0005101662512487007 0.0002550831256251429 |
| 100 90 2500 0.0010095208704887539 0.0005047604352605958 |
| # kspr2(100, 90, 5, steps=60) |
| 100 90 3000 3.535335600382311e-05 1.767667800191077e-05 |
| 100 90 3760 6.111734406393342e-08 3.055867203196533e-08 |
| 100 90 3100 1.673070087351254e-05 8.3653504367559e-06 |
| 100 90 3570 3.474759400727338e-07 1.737379700363592e-07 |
| # kspr(100, 100, 20) |
| 100 100 800 0.9084105017744525 0.5286203014039125 |
| 100 100 1600 0.1548386665118475 0.07745073909762673 |
| 100 100 900 0.8154147124661313 0.44617493329504543 |
| 100 100 1800 0.07822115797841851 0.03911245494630259 |
| 100 100 1000 0.7020569828664881 0.3691083539077194 |
| 100 100 1000 0.7020569828664881 0.3691083539077194 |
| 100 100 1300 0.36818778606286096 0.18520368254808692 |
| 100 100 800 0.9084105017744525 0.5286203014039125 |
| 100 100 1200 0.469506448503778 0.23781836509015705 |
| 100 100 1600 0.1548386665118475 0.07745073909762673 |
| 100 100 1000 0.7020569828664881 0.3691083539077194 |
| 100 100 1000 0.7020569828664881 0.3691083539077194 |
| 100 100 700 0.9684099261397212 0.6138816403400273 |
| 100 100 1500 0.21117008625127576 0.10569747923911413 |
| 100 100 600 0.9942356257694902 0.6987801650679035 |
| 100 100 1100 0.5830090612540064 0.2992770437089617 |
| 100 100 800 0.9084105017744525 0.5286203014039125 |
| 100 100 600 0.9942356257694902 0.6987801650679035 |
| 100 100 1000 0.7020569828664881 0.3691083539077194 |
| 100 100 800 0.9084105017744525 0.5286203014039125 |
| # kspr2(100, 100, 5, steps=75) |
| 100 100 2900 0.0004117410017938115 0.00020587050089724022 |
| 100 100 2500 0.0037294923618311367 0.001864746185927891 |
| 100 100 2600 0.002219935934558366 0.0011099679678142208 |
| 100 100 2700 0.0012935059781377376 0.0006467529891200971 |
| 100 100 3100 0.00012016164291946694 6.008082145973481e-05 |
| # kspr2(100, 100, 5, steps=70) |
| 100 100 3000 0.0002248739317492479 0.00011243696587464657 |
| 100 100 3200 6.281176788972264e-05 3.1405883944861374e-05 |
| 100 100 3300 3.211428734211389e-05 1.6057143671056943e-05 |
| 100 100 3500 7.850159128072286e-06 3.925079564036142e-06 |
| # kspr2(100, 100, 5, steps=65) |
| 100 100 3700 1.7527190839835072e-06 8.763595419917535e-07 |
| 100 100 4200 2.749465483696122e-08 1.3747327418480607e-08 |
| # kspr2(100, 100, 5, steps=50) |
| 100 100 5100 3.319419024623016e-12 1.6597095123115084e-12 |
| 100 100 5000 1.0024645454361508e-11 5.012322727180755e-12 |
| 100 100 5500 3.0406585087050305e-14 1.5203292543525152e-14 |
| # kspr(515, 500, 20) |
| 515 500 8185 0.9493986521608645 0.5815825961416793 |
| 515 500 7915 0.9615725209825824 0.601871942028066 |
| 515 500 7720 0.9690636734798047 0.6164340097379267 |
| 515 500 16515 0.23350385753082842 0.11693559032166966 |
| 515 500 14150 0.40736519509165603 0.20544622542022134 |
| 515 500 15750 0.28249266048886834 0.14164291536993778 |
| 515 500 14365 0.38885041334955517 0.19588222329634966 |
| 515 500 8955 0.903603296094672 0.524339532431143 |
| 515 500 11925 0.6240870483885734 0.32281246631425675 |
| 515 500 12780 0.53645777026934 0.2738050242806958 |
| 515 500 16275 0.24813390240790098 0.12430166348195652 |
| 515 500 11220 0.697534625783586 0.3666522163820955 |
| 515 500 9160 0.8887341900595557 0.5092395404996648 |
| 515 500 17940 0.15969123808843258 0.07988534277115025 |
| 515 500 21760 0.0493197290292436 0.024660214774062543 |
| 515 500 11605 0.6574794674555943 0.34235526509229514 |
| 515 500 15625 0.29114337179290417 0.1460196726063174 |
| 515 500 20290 0.07961143709393435 0.03980812865846791 |
| 515 500 11740 0.6433641257950573 0.3340198635318758 |
| 515 500 8285 0.944339176814443 0.574013022376737 |
| # kspr2(515, 500, 5, steps=460) |
| 515 500 37190 4.312475432797974e-05 2.156237716397765e-05 |
| 515 500 23725 0.02468528708275912 0.012342665062356865 |
| 515 500 21675 0.050750631293065424 0.02537570917296944 |
| 515 500 23355 0.028249692522794394 0.014124883326404823 |
| 515 500 22965 0.032490717875867006 0.01624542414831844 |
| # kspr2(515, 500, 5, steps=450) |
| 515 500 34880 0.00015657518065977083 7.828759032986811e-05 |
| 515 500 26990 0.006851609415818402 0.0034258048291346535 |
| 515 500 39945 8.308060387864811e-06 4.154030193930157e-06 |
| 515 500 30785 0.0012554915219321185 0.0006277457610908003 |
| 515 500 26840 0.007293385130763014 0.003646692721520048 |
| # kspr2(515, 500, 5, steps=400) |
| 515 500 54770 1.511195571110642e-10 7.555977855549027e-11 |
| 515 500 53040 6.463156211941191e-10 3.231578105968821e-10 |
| 515 500 54650 1.6741114699848586e-10 8.370557349919452e-11 |
| 515 500 52575 9.477200035799245e-10 4.738600017896974e-10 |
| 515 500 57850 1.0086569364127433e-11 5.04328468206092e-12 |
| # kspr(515, 515, 20) |
| 515 515 14935 0.38807451014746674 0.19548201752017033 |
| 515 515 13905 0.479034004163874 0.24297229659389263 |
| 515 515 10815 0.7857918829942412 0.4249785344115979 |
| 515 515 7725 0.9812801592459972 0.6462745124993984 |
| 515 515 9270 0.9119165633386505 0.5333147055834722 |
| 515 515 11330 0.7357540649661999 0.3909485959019169 |
| 515 515 11330 0.7357540649661999 0.3909485959019169 |
| 515 515 12360 0.6313430811283158 0.32700970276632807 |
| 515 515 22145 0.055141558408617404 0.02757132855187066 |
| 515 515 18540 0.16146324301032314 0.08077314672681853 |
| 515 515 13390 0.5281779821581033 0.2693067172881182 |
| 515 515 9785 0.8751440285488726 0.49636218852993574 |
| 515 515 16995 0.24110048586896543 0.12075921552037354 |
| 515 515 11845 0.6838779320846781 0.35824843453465616 |
| 515 515 11845 0.6838779320846781 0.35824843453465616 |
| 515 515 15450 0.34681483814007347 0.17431974406385833 |
| 515 515 13905 0.479034004163874 0.24297229659389263 |
| 515 515 12875 0.5791652849910399 0.29733660010790197 |
| 515 515 10815 0.7857918829942412 0.4249785344115979 |
| 515 515 12875 0.5791652849910399 0.29733660010790197 |
| # kspr2(515, 515, 5, steps=470) |
| 515 515 41200 7.715341729410975e-06 3.857670864705488e-06 |
| 515 515 33475 0.0005396263434587486 0.00026981317173342326 |
| 515 515 25750 0.015542998382653479 0.007771502515087006 |
| 515 515 28325 0.005593644437864241 0.002796822272300457 |
| 515 515 24205 0.027379231101175516 0.01368964821727114 |
| # kspr2(515, 515, 5, steps=460) |
| 515 515 31930 0.0011342645522721903 0.0005671322762189362 |
| 515 515 29870 0.0028903078353134577 0.0014451539213383023 |
| 515 515 33990 0.00041795499923995993 0.00020897749962141217 |
| 515 515 33990 0.00041795499923995993 0.00020897749962141217 |
| 515 515 28325 0.005593644437864241 0.002796822272300457 |
| # kspr2(515, 515, 5, steps=450) |
| 515 515 42745 2.9641506649539074e-06 1.482075332476954e-06 |
| 515 515 35020 0.0002477777699409291 0.00012388888497063505 |
| 515 515 34505 0.0003224429461502545 0.00016122147307562554 |
| 515 515 37080 8.305069523093185e-05 4.152534761546791e-05 |
| 515 515 39655 1.9376317134703097e-05 9.688158567351555e-06 |
| # kspr2(515, 515, 5, steps=440) |
| 515 515 39655 1.9376317134703097e-05 9.688158567351555e-06 |
| 515 515 41200 7.715341729410975e-06 3.857670864705488e-06 |
| 515 515 40170 1.4311681121416457e-05 7.155840560708231e-06 |
| 515 515 42230 4.093676899867059e-06 2.04683844993353e-06 |
| 515 515 39140 2.612933882401873e-05 1.3064669412009386e-05 |
| # kspr2(515, 515, 5, steps=400) |
| 515 515 59225 1.161536345492389e-11 5.807681727461947e-12 |
| 515 515 61285 1.8302055341507816e-12 9.15102767075391e-13 |
| 515 515 61285 1.8302055341507816e-12 9.15102767075391e-13 |
| 515 515 59225 1.161536345492389e-11 5.807681727461947e-12 |
| 515 515 61800 1.141356522084582e-12 5.706782610422911e-13 |
